Constructing Representations of the Nonstandardly Deformed Algebra $s\ell_\xi(2)$

The generators of the algebra $s\ell_\xi(2)$, which result from the nonstandard (Jordanian) deformation of the algebra $s\ell(2)$, are realized in the form of finite-difference operators acting in a function space. This allows realizing arbitrary-dimensional representations of $s\ell_\xi(2)$ in the polynomial space that are in one-to-one correspondence with usual matrices of an appropriate dimension. We discuss using the suggested realization to construct and investigate the universal $R$-matrix invariant with respect to the action of the algebra $s\ell_\xi(2)$.